Leibniz's Modal Metaphysics

In the main article on Leibniz, it was claimed that Leibniz's
philosophy can be seen as a reaction to the Cartesian theory of
corporeal substance and the necessitarianism of Spinoza and
Hobbes. This entry will address this second aspect of his
philosophy. In the course of his writings, Leibniz developed an
approach to questions of modality—necessity, possibility,
contingency—that not only served an important function within
his general metaphysics, epistemology, and philosophical theology but
also has continuing interest today. Indeed, it has been suggested that
20th-century developments in modal logic were either based
on Leibnizian insights or at least had a Leibnizian spirit.

In order to explain Leibniz's modal metaphysics—the metaphysics
of necessity, contingency, and possibility—we must look first at
the foundation of Leibniz's system more generally: his conception of
an individual substance. In §8 of the Discourse on
Metaphysics, Leibniz presents his classic picture, writing:

The nature of an individual substance or of a complete being is
to have a notion so complete that it is sufficient to contain and to
allow us to deduce from it all the predicates of the subject to which
this notion is attributed. (A VI iv 1540/AG 41)

In other words, each individual substance has a complete
individual concept (CIC), which contains (or from which are
deducible) all predicates true of it past, present, and
future. Leibniz asks his reader to consider the case of Alexander the
Great. On his view, God can, as it were, look at the complete
individual concept of Alexander and see that he conquered Darius and
Porus, that he was the student of Aristotle, that his armies would
march into India, and so on. For our purposes, it will suffice to
think of the CIC as the essence of an individual substance and to
think of God as able to survey all essences of all individual
substances. (The issue is, in fact, vexed; for insightful
presentations of views rivaling that presented here, see Sleigh 1990
or Cover and Hawthorne 1999.) Further, according to Leibniz, one of
the consequences of this view of the nature of an individual substance
is that no two substances can be qualitatively identical and differ
numerically. In other words, the Principle of the Identity of
Indiscernibles (PII) follows from this conception of the nature of
substance, and PII entails that, for any possible world, there is at
most one instance of a CIC.

Individual substances, of course, are parts of, or rather, members of a
world. In other words, a world is a set of individual
substances; or, as Leibniz puts in the opening line of On the
Ultimate Origination of Things, a world is a “collection of
finite things.” (G VII 302/AG 149) More specifically,
Leibniz tells Bourguet, “the universe is only a certain kind of
collection of compossibles; and the actual universe is the collection
of all possible existents, that is, of those things that form the
richest composite.” (G III 573) In saying that a world is a
set of compossible things, however, Leibniz is saying that a world is a
kind of collection of things that God could bring into
existence. For not even God can bring into existence a world in
which there is some contradiction among its members or their
properties. But this opens up the question: Just what is meant by
a contradiction in the case of the members of a world?

Let us say that two or more substances are compossible if and only
if there is no contradiction between the predicates derivable from
their CICs. For example, consider the two individuals, Don and
Ron. One of Don's properties is being the tallest man
(at time t); one of Ron's properties is also being the
tallest man (at time t). Naturally, Don and Ron cannot then
inhabit the same world. On the other hand, each could have the
property being over 2 meters tall and be members of the same
world. Now in Leibniz's fully developed metaphysics this
example might not be considered a good one, since it is most likely the
case that Leibnizian individuals are not to be thought of as
constituted by such relational properties. Rather than thinking
of compossibility in terms of the properties of substances, it might be
easier to think of it in terms of the perceptions of substances.
Certainly, Don and Ron cannot be said to be members of the same world
if Don perceives the moon landing of Apollo 11 on July 20, 1969 and Ron
does not (or would not)—and not simply because he does not have
a television set, but because on his July 20, 1969, there is
no United States of America, let alone a space program. From
this, it should also be clear that the compossibility of substances in
a world is another manifestation of Leibniz's thesis of the
universal harmony of perceptions of substances.

A possible world, however, is not simply a set of compossible
individuals. According to Leibniz, a possible world also entails
certain laws of nature. As Leibniz says to Arnauld in a letter
from 14 July 1686,

I think there is an infinity of possible ways in which to create the
world, according to the different designs which God could form, and
that each possible world depends on certain principal designs or
purposes of God which are distinctive of it, that is, certain primary
free decrees (conceived sub ratione possibilitatis) or certain
laws of the general order of this possible universe
with which they are in accord and whose concept they determine, as they
do also the concepts of all the individual substances which must enter
into this same universe. (G II 51/L 333)

Leibniz's basic idea here should conform closely with our
intuitions. Imagine God's considering a set of
individuals {a, b, c, d}. From God's point of view
he could choose to actualize this world with one set, L*, of
laws of nature or with another set of laws, L**. And
this choice represents a choice between two possible worlds. This
is similar to our saying that we would have a different world
if the gravitational constant were different. Now, this way of
speaking is not exactly right, for on Leibniz's view, the
different sets of laws would ultimately produce different properties
and perceptions with the individual substances. As a result, the
individuals in the worlds governed by L* and L**
would strictly speaking be different.

The reason Leibniz mentions the different laws governing the different
possible worlds is that the systems of laws and their effects serve as
criteria by which God chooses a world. We know that, for Leibniz,
God chooses the “best of all possible worlds.” In
§6 the Discourse on Metaphysics, however, we learn that
this means that God chooses the world that is simplest in hypotheses
(or laws) and richest in phenomena. Thus, while one might be
tempted to see natural laws as derivative of the actual properties and
perceptions of individual substances, in fact they are objects of
God's choice.

When Leibniz speaks of a possible world, he means a set of
compossible, finite things that God could have brought into
existence if he were not constrained by the goodness that is
part of his nature. The actual world, on the other hand, is
simply that set of finite things that is instantiated by God, because
it is greatest in goodness, reality and perfection. Naturally, the
fact that we are here experiencing this world – the actual
world – means that there is at least one possible world. So are
there others?

Yes, indeed, there are. At least Leibniz thinks so. In his view, as we
saw above, there are an infinite number of possible worlds –
worlds that God did not see fit to bring into existence. Now, given
that Leibniz's safe claim is that “[t]here are as many possible
worlds as there are series of things that can be conceived that do not
imply a contradiction,” (Grua 390) it might still be the case
that there is only one possible world – only one set of
essences that implies no contradiction. If we accept the claim that a
possible world is simply any set of compossible individuals (i.e. a
set of individuals whose properties or perceptions do not contradict
each other), then there is a rather trivial way to show that there are
an infinite number of possible worlds. Namely, we just have an
infinity of one-object worlds: thus w1 contains a
blue, 8lb. bowling ball; w2, a red, 10lb. bowling
ball; w3, a pepperoni
pizza; w4, a bicycle; and so on. We could even
imagine worlds with two, three, or more objects.

Now, Leibniz's reasons for proposing an infinity of possible worlds
are somewhat different. In his short essay On Contingency
(De contingentia, 1689?), Leibniz makes the following
claim:

One must certainly hold that not all possibles attain existence,
otherwise one could imagine no novel that did not exist in some place
and at some time. Indeed, it does not seem possible for all
possible things to exist, since they get in one another's
way. There are, in fact, an infinite number of series of possible
things. Moreover, one series certainly cannot be contained within
another, since each and every one of them is complete. (A VI iv 1651/AG
29)

The point here is that there are unactualized possibles as
exemplified in works of fiction. In other words, a work of fiction
represents some way the world could be. (To be precise, works
of fiction represent partial ways worlds could be since they
do not (and cannot) depict complete or total
worlds. For example, was Lincoln shot in the world described
by Moby-Dick? We don't know.) But, insofar as these
possibles conflict among themselves, it is clear that not all
possibles are compossible. Rather, as we saw above, sets of
compossible individuals are Leibniz's possible worlds. If we add to
this picture the idea that each individual has a complete individual
concept – that is, a determinate concept – which is
sufficient to distinguish it from every other possible world, then we
see that possible individuals are tied to determinate possible
worlds.

But what is the character of these non-actualized possibles?
The most natural assumption is that they are like individual substances
as characterized by Leibniz in Discourse on Metaphysics
§8, that is, as having complete individual concepts. In
other words, all individuals (actual or merely possible) have
determinate essences. In the case of merely possible individuals,
however, their being is contained solely in the divine mind.
Consider Leibniz's claim in the Theodicy §189:
“In the region of the eternal verities are found all the
possibles.” (G VI 229/H 246) And, in §44 of the
Monadology, in the middle of his argument for God's
necessary existence, Leibniz says, “if there is reality in
essences or possibles, or indeed, in eternal truths, this reality must
be grounded in something existent and actual, and consequently, it must
be grounded in the existence of the necessary being, in whom essence
involves existence, that is, in whom possible being is sufficient for
actual being.” (G VI 614/AG 218) In other words, there will
be determinate essences of some substances that are actualized in the
world as well as determinate essences of substances that exist solely
in the divine intellect.

By way of contrast, Spinoza argues in the Ethics (Ip33) that
there are no unactualized possibles. In the case of a story
depicting another “reality,” we have only partial and
confused knowledge of the world depicted. If we were to
have true knowledge of the way all the characters and their actions
extend backward and forward in time, we could ultimately arrive at some
contradiction. Moreover, Spinoza holds that everything that is
truly possible will be expressed at some point as God or nature
expresses its infinite essence. That is, since God is a substance
of infinite attributes expressed in infinite ways, everything that is
possible finds existence at some point in this
world. Of course, this difference between Leibniz and Spinoza is
largely attributable to Leibniz's adherence to what Spinoza finds
so wrong: the anthropomorphic conception of God and the attendant
distinction between divine intellect and will, which is what allows for
God's supposed contemplation of non-existent possibles.

In Meaning and Necessity, Rudolf Carnap suggests that a
Leibnizian possible world is represented by his
state-descriptions: a class of sentences containing, for
every atomic sentence, either it or its negation. In other words, for
each possible world there is a series of propositions that will fully
describe that world. The idea of a possible world as being such a set
of sentences or propositions leads naturally to the notion of a
“world-book,” a term employed by Alvin Plantinga
(The Nature of Necessity). Lest such devices seem
anachronistic, it should be pointed out that, in the fascinating
conclusion to the Theodicy, Leibniz speaks in a similar way;
indeed, Leibniz's parable is something that one might imagine has come
straight from Jorge Luis Borges (cf. “The Library of
Babel”). The story concerns Theodorus, a high priest present
when Sextus Tarquinius complains to Jupiter about his fate. (Sextus
was the son of the last king of Rome, whose crime of raping Lucretia
so incensed Brutus that he led a revolt that ultimately abolished the
monarchy and began the Roman Republic.) Theodorus is moved by Sextus'
complaint and is sent to receive instruction at the temple of Pallas
Athena where he is shown “the palace of the fates.”
According to Athena, “Here are representations not only of that
which happens but also of all that which is possible. Jupiter, having
surveyed them before the beginning of the existing world, classified
the possibilities into worlds, and chose the best of all.”
(Theodicy §414: G VI 363/H 370) She continues,

I have only to speak, and we shall see a whole world that my father
might have produced, wherein will be represented anything that can be
asked of him; and in this way one may know also what would happen if
any particular possibility should attain unto existence. And
whenever the conditions are not determinate enough, there will be as
many such worlds differing from one another as one shall wish, which
will answer differently the same question, in as many ways as
possible… But if you put a case that differs from the actual
world only in one single definite thing and in its results, a certain
one of those determinate worlds will answer you. These worlds are
all here, that is, in ideas. I will show you some, wherein shall
be found, not absolutely the same Sextus as you have seen (that is not
possible, he carries with him always that which he shall be) but
several Sextuses resembling him, possessing all that is already in him
imperceptibly, nor in consequence all that shall yet happen to
him… (Theodicy §414: G VI 363/H 370–71)

Theodorus is led into one of the halls of the palace and, observing
a great volume of writings in the hall, asks what it is.
“It is,” Athena tells him, “the history of this world
which we are now visiting…; it is the book of fates.”
(Theodicy §415: G VI 363/H 371–72) And, finally, we
have an argument for the infinity of worlds wrapped in a fantasy
tale:

The halls rose in a pyramid, becoming even more beautiful as one
mounted towards the apex, and representing more beautiful worlds.
Finally they reached the highest one which completed the pyramid, and
which was the most beautiful of all: for the pyramid had a beginning,
but one could not see its end; it had an apex, but no base; it went on
increasing to infinity. That is (as the Goddess explained)
because amongst an endless number of possible worlds there is the best
of all, else would God not have determined to create any; but there is
not any one which has not also less perfect worlds below it: that is
why the pyramid goes on descending to infinity. (Theodicy
§416: G VI 364/H 372)

Leibniz makes clear here his basic view of God's
obligation to choose the best world possible, as well as his
view that, if there were not a single best world, no world at all
would have been brought into existence. At the same time, the argument
for the infinity of possible worlds given here is rather comical:
(granted, there must be one best world) for any world you can imagine
(or find in the pyramid), there is one that is worse. So much for
Leibniz the optimist!

The world-books are on permanent display in the divine intellect.
This is what Leibniz means when he says that they reside in the realm
of eternal verities. But one thing should be absolutely clear:
Leibniz is no modal realist à la David Lewis. Although
Leibniz claims that there are an infinity of possible worlds,
he does not mean that infinitely many possible worlds exist in the same
way as this (actual) world does, or that infinitely many worlds are
running, as it were, parallel to this one, or that “actual”
is an indexical expression like “here” and “now.”
The existence claim commits Leibniz only to the existence of different ways
the world could be and to the shelving of these world-books in the
infinite and eternal library of the divine mind. As he puts it in
the same letter to Arnauld, “there is no other reality in pure
possibles than the reality they have in the divine
understanding.” (G II 45/AG 75) But it is crucial to
Leibniz's position that there be one and only one actual
world, the best of all possible worlds. As we have seen, God is
obligated to bring this one world into existence. And,
we have also seen that, according to Leibniz, if there were no uniquely
best world, then God would not have brought any world into
existence. (And God could not simply play Eenee, Meenee,
Mainee, Mo! with two worlds; he must, according to the Principle
of Sufficient Reason, have a ground for his decision.) Further,
there cannot be two worlds that are absolutely equal in terms of their
degrees of perfection, for God, by virtue of his omnipotence and
omniscience, must be able to determine some distinction
between the worlds. And if God had actualized more than one world
and they had been of different degrees of perfection, then God would
have brought into existence that which is less perfect than possible (a
violation of the requirements of divine benevolence). (Concerning
the reasons for this world, more below.)

One reason that Leibniz's conception of possible worlds has
attracted the sympathetic attention of some contemporary philosophers
and has proven appealing is that it appears to foreshadow the
developments in possible-worlds semantics. According to this
view, our basic modal concepts—necessity, contingency,
possibility and impossibility—can be defined in
straightforwardly non-modal terms.

Possibility: A proposition is possible if and only if it
is true in some possible world. A being is possible if and only if it
exists in some possible world.

Contingency: A proposition is contingently true if and
only if it is true in this world and false in another world. A
proposition is contingent if its contrary does not imply a
contradiction.

Necessity: A proposition is necessarily true if and only
if it is true in every possible world.

Impossibility: A proposition is impossible if and only if
it is not true in any possible world.

But does Leibniz's account of necessity and contingency really
amount to possible-worlds semantics for modality avant la
lettre? While Leibniz had all the tools at his disposal to
develop such an account of modality, he did not, or, at least, he did
not do so explicitly in any texts. Rather, his account of the
nature of necessity and contingency has more to do with his account of
the nature of truth and the analysis of propositions. More
specifically, it has to do with his doctrine of infinite
analysis. In his piece On Contingency,
Leibniz writes,

[I]n necessary propositions, when the analysis is continued
indefinitely, it arrives at an equation that is an identity… But
in contingent propositions one continues the analysis to infinity
through reasons for reasons, so that one never has a complete
demonstration, though there is always, underneath, a reason for the
truth, but the reason is understood completely by God, who alone
traverses the infinite series in one stroke of mind. (A VI iv 1650/AG
28)

In other words, a proposition is necessary (or expresses a necessary
truth) if, in analyzing it, one arrives at a statement of
identities. A simple example can be found in arithmetic:
“2+2 = 4.” Since “2 = 1+1” and “4 =
1+1+1+1”, we can easily show that the original statement can be
reduced to “1+1+1+1 = 1+1+1+1.” Here we have an
obvious case of an identity and one where we can say that the concept
of the predicate – in this case, “4” – is
contained is contained in the subject, “2+2” (or
“(1+1) + (1+1)”).

It should be clear that Leibniz's definition of what is
necessary will be adopted by Kant, but Kant will call
this analytic. (On the other hand, Kant famously rejects
the idea that the arithmetic statement given above (or any arithmetic
statement) is analytic. Although this is a topic of some
controversy, the majority of jurors have a returned a verdict in favor
of Leibniz's classificatory scheme and against that of Kant.)

A
true proposition that is contingent is one in which it can
never be demonstrated that the subject and predicate terms are
reducible to identities. Indeed, according to Leibniz, the
analysis of these concepts can be carried on to infinity. While
this might seem vague, Leibniz often compares the distinction between
necessary and contingent truths to rational and irrational numbers.

[I]n proportions, while the analysis sometimes comes to an end, and
arrives at a common measure, namely, one that measures out each term of
the proportion through exact repetitions of itself, in other cases the
analysis can be continued to infinity, as happens in the comparison
between a rational number and an irrational number, such as the
comparison of the side and the diagonal of a square. So, similarly,
truths are sometimes provable, that is, necessary, and sometimes they
are free or contingent, and so cannot be reduced by any analysis to an
identity, to a common measure, as it were. And this is an essential
distinction, both for proportions and for truths. (A VI iv
1657/AG 97)

Although “infinite analysis” might still seem a rather
elusive idea, the driving thought should not be so difficult.
The reason for any contingently true proposition is to be
found in another contingently true proposition, and this chain of
reasons goes back ultimately to the creation of the world (or rather to
God's free choice of this particular world). We,
with our finite minds, are not able to grasp this chain of reasons, but
God can do so.

But in contingent truths, even though the predicate is in the
subject, this can never be demonstrated, nor can a proposition ever be
reduced [revocari] to an equality or to an identity, but the
resolution proceeds to infinity, God alone seeing, not the end of the
resolution, of course, which does not exist, but the connection of the
terms or the containment of the predicate in the subject, since he sees
whatever is in the series. Indeed, this very truth was derived in part
from his intellect, in part from his will, and it expresses his
infinite perfection and the harmony of the entire series of things in
its own particular way. (A VI iv 1656/AG 96)

Leibniz's definition of a possibility is simply a
proposition that can be shown to be such that a contradiction will
never arise in its analysis. (A VI iv 758/LLP 61) And an
impossibility, not surprisingly, is defined as a proposition that can
be demonstrated to generate a contradiction in its analysis.

It was claimed above that Leibniz does not explicitly adopt the kind of
possible-worlds semantics endorsed by Lewis and others in his own
definitions and explanations of our basic modal concepts. But it
is easy to show that Leibniz's account of these modal concepts
can be translated into the now standard possible-worlds
semantics. Consider the way Leibniz distinguishes necessary and
contingent truths in §13 of the Discourse on
Metaphysics.

The one whose contrary implies a contradiction is absolutely
necessary; this deduction occurs in the eternal truths, for example,
the truths of geometry. The other is necessary only ex
hypothesi and, so to speak, accidentally, but it is contingent in
itself, since its contrary does not imply a contradiction. And this
connection is based not purely on ideas and God's simple understanding,
but on his free decrees and on the sequence of the universe. (A VI iv
1547/AG 45)

For it will be found that the demonstration of this predicate of
Caesar is not as absolute as those of numbers or of geometry, but that
it supposes the sequence of things that God has freely chosen, a
sequence based on God's first free decree always to do what is most
perfect and on God's decree with respect to human nature, following out
of the first decree, that man will always do (although freely) that
which appears to be best. But every truth based on these kinds of
decrees is contingent, even though it is certain; for these decrees do
not change the possibility of things, and, as I have already said, even
though it is certain that God always chooses the best, this does not
prevent something less perfect from being and remaining possible in
itself, even though it will not happen, since it is not its
impossibility but its imperfection which causes it to be rejected. And
nothing is necessary whose contrary is possible. (A VI iv 1548/AG
46)

The crucial idea here is that a proposition is contingently true in
this world when it is somehow dependent upon the first free decree of
God, that is, when the reason for the truth of the
proposition is to be located in the actualization of this
particular world. There is another world, W*, existing in the
infinite library of world-books, which is such that if God
had brought that world, W*, into existence P would
be false. In other words, a proposition is contingently true when it
is true in that world and false in some other world. As mentioned
above, however, Leibniz defines a possible proposition in another text
from this period as a proposition which will never result in a
contradiction in its analysis, and given his account of worlds, this
simply means that the proposition is true in some world. Further,
since necessary truths are not dependent upon the first free
decree of God but are instead revealed by analysis to be identities,
they are in fact propositions that are true in all possible
worlds. And so, while our basic modal concepts are explained in terms
of the in-esse doctrine of truth (i.e. the
Predicate-in-Notion Principle) and the notion of infinite analysis (in
the case of contingency), it is a not a great jump to possible-worlds
semantics.

It should probably not be surprising that Leibniz's explication of the
nature of the distinction between necessary and contingent truths can
be translated into the terms of contemporary possible-worlds
semantics. For Leibniz tells us in On Freedom (De
libertate... 1689?) that he first came to think of the
nature of possibilia in terms of fictional worlds, worlds
that have existence in a somewhat tenuous sense. “But the
consideration of possibles, which are not, were not, and will not be,
brought me back from this precipice [Spinoza's necessitarianism]. For
if there are certain possibles that never exist, then the things that
exist, at any rate, are not always necessary, for otherwise it would
be impossible for others to exist in their place, and thus, everything
that never exists would be impossible.” (A VI iv
1653–54/AG 94) It was only later that he began to conceive of
the distinction between necessary and contingent truths in terms of
finite and infinite analysis. In the end, then, we can say that the
doctrine of infinite analysis is dependent upon the doctrine of the
infinity of possible worlds.

Leibniz's logical conception of the nature of substance,
according to which each individual substance has a concept so complete
that it contains all predicates true of it past, present, and future
(or from which all its predicates are deducible), also seems to push
him to endorse a strong version of essentialism. Just
how strong this essentialism is has been the subject of debate among
scholars of Leibniz's thought.

Call essentialism the doctrine that for any individual
substance, x, there is a property P of x
such that, necessarily, if x exists, then x
has P. In other words, there is some property that
is essential to x. For example, one could argue that
humanity is essential to Caesar; and if Caesar (somehow) were to lose
the property of being a human being, Caesar would cease to be
Caesar.

Call superessentialism the doctrine that for any
individual substance, x, and for any
property P of x, necessarily,
if x exists, then x has P. In
other words, every property is essential
to x. For example, one might imagine
that crosser of the Rubicon or possessor of 12,147 hairs
on his head on the Ides of March, 44 B.C.E. were properties that,
were they different, the Caesar of our world would no longer
exist. (For the sake of argument, assume that the head-hair count is
true; it is only supposed to get at some seemingly trivial property.)
Or, put differently, if those properties were different, the Caesars
would be genuinely different individual substances.

Now, it certainly seems that Leibniz's view is that, indeed,
every property of an individual substance is essential to
it.

This very point is something that Antoine Arnauld noticed
immediately upon reading the Discourse on Metaphysics.
(More exactly, Arnauld read only what are now usually presented as
brief synopses of the individual sections.) As he wrote to
Leibniz, “Since it is impossible that I should not always have
remained myself, whether I had married or lived in celibacy,
the individual concept of myself contained neither of these
two states; just as it is well to infer: this block of marble is the
same whether it be at rest or be moved; therefore neither rest nor
motion is contained in its individual concept.” (G II 30)
Arnauld's point is quite simply that the property of being
celibate is not essential to him or to his concept
because he would still be Arnauld even if he had married and had
children.

Leibniz's response takes us into some fascinating metaphysical
territory. Returning to his original example of Adam and his
sins, Leibniz writes the following:

I have said that all human events can be deduced not simply by
assuming the creation of a vague Adam, but by assuming the creation of
an Adam determined with respect to all these circumstances, chosen from
among an infinity of possible Adams. This has given Arnauld the
occasion to object, not without reason, that it is as difficult to
conceive of several Adams, taking Adam as a particular nature, as it is
to conceive of several mes. I agree, but when speaking of several
Adams, I was not taking Adam as a determinate individual. I must
therefore explain myself. This is what I meant. When one considers in
Adam a part of his predicates, for example, that he is the first man,
set in a garden of pleasure, from whose side God fashioned a woman, and
similar things conceived sub ratione generalitatis, in a
general way (that is to say, without naming Eve, Paradise, and other
circumstances that fix individuality), and when one calls Adam the
person to whom these predicates are attributed, all this is not
sufficient to determine the individual, for there can be an infinity of
Adams, that is, an infinity of possible persons, different from one
another, whom this fits. Far from disagreeing with what Arnauld says
against this multiplicity of the same individual, I myself used this to
make it better understood that the nature of an individual must be
complete and determinate. I am even quite convinced of what Saint
Thomas had already taught about intelligences, which I hold to apply
generally, namely, that it is not possible for there to be two
individuals entirely alike, or differing only numerically. Therefore,
we must not conceive of a vague Adam, that is, a person to whom certain
attributes of Adam belong, when we are concerned with determining
whether all human events follow from his assumption; rather, we must
attribute to him a notion so complete that everything that can be
attributed to him can be deduced from it. Now, there is no room for
doubting that God can form such a notion of him, or rather that he
finds it already formed in the realm of possibles, that is, in his
understanding.

It, therefore, also follows that he would
not have been our Adam, but another Adam, had other events happened to
him, for nothing prevents us from saying that he would be another.
Therefore, he is another. (G II 41–42/AG 72–73)

Leibniz's point is that, since the Adam of the actual world (call him
“Adam@”) has a complete concept containing all
of his properties and since Adam@ (or any substance)
expresses the entire world of which he is a member, Adam@
could not exist in a different world. Moreover, if any of
Adam@'s properties were somehow changed, then the resulting
being would not be Adam@. This is indeed an important
consequence of his Principle of the Identity of Indiscernibles. When
we speak of the Adam who brought sin into the world and an Adam who
did not, we cannot, strictly speaking, be referring to the same
individual. And that failure of identical reference is the key to
seeing that all of Adam's properties are essential to him. Leibniz
makes this point about as clearly as he makes any point in §30 of
the Discourse on Metaphysics in his discussion of Judas' sin:
“But someone else will say, why is it that this man will
assuredly commit this sin? The reply is easy: otherwise he would not
be this man.” (A VI iv 1576/AG 61) In other words, Leibniz seems
to deny the possibility of “transworld-individuals” and
asserts instead that every individual is “world-bound.”
Nevertheless, Leibniz argues that there are “vague Adams,”
that is, quasi-individuals which exist in more than one world. And
when we imagine other possible worlds in which “Adam” does
not sin or eats the forbidden donut, we are imagining only an
incomplete or vague “Adam” who is the individual in that
world – not the same individual. That is, the
“vague Adams” are only quasi-individuals because their
individual concepts are not complete. Indeed, when Leibniz speaks of
the “vague Adams,” what he has in mind is some set
properties that is common to a number of individuals:
Adam@, Adamw′ (i.e. Adam in
world′), Adamw″,
Adamw′′′, and so on. In the
terminology of David Lewis's modal theory, they are the
“counterparts” of Adam in other possible worlds. Strictly
speaking, however, only individuals with complete individual concepts
are denizens of other possible worlds; quasi-individuals per se cannot
be said to exist. But an incomplete concept can be used to delimit a
set of counterparts that do exist with complete individual concepts in
different possible worlds. And lest it be thought that talk of the
idea of a “vague Adam” is limited to his discussion in the
1680s with Arnauld about modal matters, it should be noted that
Leibniz makes much the same point 20 years later in the concluding
sections of the
Theodicy discussed and quoted above when he writes of the
“several Sextuses” that are to be found in the palace
containing the books of fates. All of this speaks very strongly
for attributing the doctrine of superessentialism to Leibniz throughout
his life as well as the denial of the doctrine of transworld
identity.

But if we attribute the doctrine of superessentialism to Leibniz, then
it would seem that there will be a difficulty in distinguishing those
properties that traditionally were thought to be essential to an
individual and those that were thought to be mere accidents. In
other words, if all properties are essential, on Leibniz's view,
is there any difference between his humanity and his
wearing a fluffy silk shirt on 1 January 1700? Not
surprisingly, Leibniz has a solution to this apparent problem. In an
important work on logic from the period of the Discourse on
Metaphysics and Correspondence with Arnauld, the General
Inquiries about the Analysis of Concepts and of Truths
(Generales Inquisitiones de Analysi Notionum et Veritatum,
1686), Leibniz makes the standard, Aristotelian distinction between
essential properties and accidents, saying “that thing which is
called ‘a man’ cannot cease to be a man except by
annihilation; but someone can begin or cease to be a king, or learned,
though he himself remains the same.” (A VI iv 740/LLP 47) The
important point here is the species to which an individual
belongs contributes one level of properties to an individual; but, of
course, these are properties that are held in common by all members of
that particular species. Therefore, for example, Adam is not only a
man, but necessarily also rational and, to use the Aristotelian
chestnut, a featherless biped. Following Mondadori (1993), let us
call being a human being a specific essential
property. But there may also be individuating essential
properties, those which single x out from
the other members of the same species and which are nevertheless such
that, lacking them, x would no longer be
x. For example, consider several counterpart
Adams: one who brought no sin into the world, one who did so by eating
the forbidden donut, etc. As we have said, they cannot be
identical to Adam@, which is another way of saying that
Adam@ would cease to be Adam@ if he no longer
brought sin into the world by eating the forbidden fruit. But now
consider a Plantinga-inspired example: the alligator who brought sin
into the world. Could the alligator count as a counterpart of
Adam@? No, for lacking the property of humanity, there are
simply no counterparts of Adam@. In support of this view,
consider On Freedom, Fate and the Grace of God (De
libertate, fato, gratia Dei, 1686/87), where Leibniz first has a
critic of his view say that, “God … has in his intellect
a notion or an idea of Peter as perfect as possible containing all
truths concerning Peter, the objective reality of which constitutes
the complete nature or essence of Peter, and accordingly, to deny is
essential to Peter and is foreknown by God.” Leibniz's response
employs the distinction between necessary and contingent
properties:

there is contained in this complete notion of a possible Peter,
which I concede is observed by God, not only the essential or the
necessary, namely, that which flows from incomplete or specific
notions, and which are demonstrated from terms so that the contrary
implies a contradiction, but also the existential or contingent so to
speak are contained therein, because it is of the nature of an
individual substance that its nature be perfect and complete. (A VI iv
1600)

While the first passage seems to be Leibniz's position, he
actually finesses this view in the second passage. Those
properties that are said to be necessary or essential are actually what
were called above the specific essential properties.
Thus, Peter's specific essential properties include being a human
being and what follows from that, for example, being rational.
The crucial feature of these properties is that their absence
means that the individual would be annihilated entirely; for example,
if humanity were somehow stripped from Peter's complete
individual concept, Peter would cease to exist
completely. Those properties that are said to be
contingent or existential are all the myriad properties that
individuate Peter and that make Peter the particular person that he
is. As Leibniz says, they are what fill out Peter's
complete individual concept. Now, these properties can still be
considered essential in the sense relevant to Leibniz's
superessentialism, but in the following way (similar to what was said
above about Adam@): if such a property, for example,
denying Christ, were stripped from Peter's complete
individual concept, Peter would cease to be Peter. In other
words, imagine Peter's notion, containing, among other things,
humanity, being a disciple of Christ, being the
founder of the church, and being a denier of
Christ. Leibniz's point seems to be that we
could peer into a nearby possible world where a
Peter-counterpart did not deny Christ. But there is no nearby
possible world in which a Peter was the alligator or marmoset that
denied Christ.

If, however, this is Leibniz's view, then it might seem that
we have a problem: the specific essential properties of an individual
are few; the individuating essential properties are many; and the
specific essential properties are in fact so few that they do little
work. Yet, it should be emphasized that, for Leibniz, there is
something very important about drawing a line between human beings and
other animals: we are rational, while they are not; we are capable of
morality, while they are not. This view comes out most clearly in
Leibniz's New Essays, where he is trying to undermine
Locke's deep anti-essentialism: “as we know the inner
essence of man, namely reason, which resides in the individual man and
is present in all men, and as we find among us no fixed inner feature
which generates a subdivision, we have no grounds for thinking that the
truth about their inner natures implies that there is any essential
specific difference among men.” (A VI, vi, 325–26/RB
325–26) In other words, there are certain properties within us
that necessarily differentiate us from all other species and those that
differentiate us from all other individuals within that species.
In this regard, Leibniz is a traditionalist, upholding a real,
essential distinction between human beings and other creatures.
Yet, insofar as he believes that all properties of an
individual are essential to that individual, Leibniz is radical.

In On Contingency, Leibniz remarks that “there are
two labyrinths of the human mind, one concerning the composition of the
continuum, and the other concerning the nature of freedom, and they
arise from the same source, infinity.” (A VI iv 1654/AG 95)
Someone coming upon this passage for the first time might be puzzled by
Leibniz's claim. Why, after all, should the labyrinth of
the nature of freedom be related to infinity? Given our
discussion above concerning contingency and infinite analysis, the
answer should be relatively clear.

Leibniz's account of modality opens the way for him to present a
distinctive kind of compatibilist theory of free will. For, according
to Leibniz, Caesar's crossing of the Rubicon was a free act insofar as
it spontaneously flowed from his own individual nature or was part of
his complete concept and insofar as it represented Caesar's choice of
what he perceived to be the best option for him at the time. This
action was not necessary – and therefore contingent
– because its contrary (for example, staying in Gaul) does
not imply a contradiction. In saying that there is no contradiction,
Leibniz means that either property or action – crossing the
Rubicon or remaining in Gaul – could co-exist within a complete
set of properties of a Caesar. But as we saw above, there are
some properties that, were they changed, the individual would cease to
be. Thus, for example, it is a fair bet that Caesar was not free to
become a trout. Put differently, we can say that, while Caesar crossed
the Rubicon in this world and thus began the Roman Civil
Wars, there is another possible world in which a Caesar
did not cross the Rubicon. (Again, the
“existence” of the other possible world is meant only to
imply that there is some set of compossible essences that include the
Caesar-counterpart who does not cross the Rubicon.)

Leibniz's conception of substance, according to which each
individual has a complete individual concept, still seems remarkably
necessitarian. After all, even predicates related to my
future actions are now contained within my complete individual
concept. This smacks of determinism and raises in its own way the
problem of future contingents. As mentioned above, Leibniz claims
that we are free in part precisely because our actions follow from our
very natures with complete spontaneity. But also, according to
Leibniz, God “inclines our souls without necessitating
them.” Indeed, in the Discourse on Metaphysics,
Leibniz claims that the actions of an individual are certain
but not necessary. They are, Leibniz argues, certain ex
hypothesi—that is, they are certain given the creation or
instantiation of this particular world. God saw that Caesar would
cross the Rubicon, that Judas would betray Christ, that Adam would sin,
and so on; each of these acts and an infinity of others were included
in each individual's complete concept; and yet God chose this
world in which such actions would certainly take place.
But, at the same time, since the contraries of any such actions do not
imply contradictions, they are not necessary. God, in choosing a
possible world, chooses all the essences of all the actual individuals,
each of which has its program, according to which it acts spontaneously
and freely. While it is still a program or a complete concept, on
Leibniz's view, that does imply determination.

Leibniz is famous for his “optimism,” that is, for the
thesis that this is the best of all possible worlds. According to
Leibniz, God surveyed the infinitely many possible worlds,
determined which was best, and instantiated it or made it actual.
In an important article, “Theories of Actuality,” Robert
Merrihew Adams dubs this the “Divine Choice Theory” of
actuality. In the main article on Leibniz, the reasons for this
view are presented. But it is important to see that there are
several factors that contribute to God's choice: first, according
to Leibniz, God chose the world that was simplest in hypotheses (or
laws) and richest in phenomena; second, it is claimed that God was
chiefly concerned with the happiness of minds; third, since (it is
argued) God sought to have the maximum perspectives on the universe,
the world is a plenum, filled with minds each of which expresses the
world from its own point of view.

Although the Divine Choice Theory does seem to be Leibniz's preferred
way to explain the origin of this—the actual—world, he
does offer another explanation that deserves comment. This is the
doctrine of striving possibles. According to this view, as
presented principally in On the Ultimate Origination of
Things (De rerum originatione radicali, 1697), each
essence naturally strives for existence, and the actual world is
simply the final battlefield after all possible essences have engaged
in mortal combat for survival. In short, this is metaphysical
Darwinism, in which the most perfect (and mutually compatible)
essences survive to constitute a world. Consider the following:

Furthermore, in order to explain a bit more distinctly how temporal,
contingent, or physical truths arise from eternal, essential or
metaphysical truths, we must first acknowledge that since something
rather than nothing exists, there is a certain urge for existence or
(so to speak) a straining toward existence in possible things or in
possibility or essence itself; in a word, essence in and of itself
strives for existence. Furthermore, it follows from this that all
possibles, that is, everything that expresses essence or possible
reality, strive with equal right for existence in proportion to the
amount of essence or reality or the degree of perfection they contain,
for perfection is nothing but the amount of essence.

From
this it is obvious that of the infinite combinations of possibilities
and possible series, the one that exists is the one through which the
most essence or possibility is brought into existence. In practical
affairs one always follows the decision rule in accordance with which
one ought to seek the maximum or the minimum: namely, one prefers the
maximum effect at the minimum cost, so to speak. (G VII 303/AG
150)

Since the theory of Striving Possibles seems so obviously to
conflict with the Divine Choice Theory and since the latter is so much
a part of Leibniz's mature system, we seem to have good reason to
question how seriously to take this view. (The classic articles
on this issue are those by Shields and Blumenfeld listed in the
bibliography.) There is, however, a common way to reconcile the
two views: the Divine Choice Theory literally explains the origin of
this world, and the Striving Possibles Theory is merely a
metaphor. But a metaphor for what? Answer: for the moral
evaluation taking place in the divine intellect. In other words,
God ought to be understood as surveying not simply all worlds (sets of
compossible essences) prior to creation but also, in some sense,
individual essences; and those essences which individually are most
perfect and which collectively can form a world are in fact elected for
existence.

In conclusion, it has been claimed throughout this piece that
Leibniz advances his unique views on modality in opposition to the
views of Hobbes and Spinoza. In short, the modal metaphysics we
find in Leibniz's system is a result of the attempt to combine
the insights of a mechanistic (and therefore deterministic) world-view
with the demands of orthodox Christianity. There are a number of
important particular points to bring out here. First, on
Spinoza's view, everything that is possible is actual; that is,
there are no unactualized possibilities. To claim that some
particular thing or event could have been otherwise or to claim that
the world itself could have been otherwise is simply to make an
assertion without adequate knowledge. Indeed, one of the
cornerstones of Spinoza's philosophy is the view that, if one has
knowledge of the third kind, then one will recognize that
everything happens out of the necessity of the divine
nature. Second, if the Divine Choice Theory is the preferred
account of the origin of this actual world, then Leibniz stands in
opposition to Spinoza both because the Divine Choice Theory entails the
existence of non-actualized possible worlds and also because it clearly
entails a God that is anthropomorphic and transcendent. In other
words, the Divine Choice Theory requires a God in whom intellect and
will are distinct. Third, Leibniz's accounts of necessity
and contingency are, obviously, in service of his commitment to the
real freedom of human beings – and this in the face of the
mechanistic world-view to which he otherwise adhered. This should
be in no way surprising because Leibniz, unlike Hobbes and Spinoza,
upheld the basic tenets of Christianity and had to explain how freedom
and responsibility could be attributed to an individual, whose very
nature (following Leibniz's account of truth) entailed all
properties, past, present, and future.